When there is poor-quality or distorted sensor data that is being used to measure a time-varying process, a nonlinear filter/estimator extracts underlying important time-varying information. For example, a camera pointed at a road in front of a car driving on a foggy night may generate poor-quality data of the road location relative to the car, and the road location may be time-varying due to steering movements and curves in the road. A nonlinear filter may be useful for estimating the road location relative to the car in order to assist the driver to make corrective movements. In another example, radar is used to track the position of a moving object. A nonlinear filtering algorithm would be useful for estimating the location of the moving object from poor-quality and distorted radar.
Common types of noise include sensor noise from cameras and other imaging systems, radar, ultrasonic range sensors, X-rays, microphones, and ambient sources of noise. Common types of distortion include quantization (encoding continuous measurements using a small number of bits in a computer). The Bayes-optimal nonlinear filtering algorithm is at least as good as current algorithms at handling noise, and is much better at handling quantization and other computational distortions.